Order of Operations (4 Examples) | PEMDAS | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover the order of operations and we have four examples that we're going to go through together in order to get this down now remember the order of operations are a set of rules or instructions that we need to follow in order to solve problems with multiple operations and steps correctly it goes parentheses exponents multiplication or division and then addition or subtraction so we can remember those steps with the following acronym pemdas now i do have an intro video to the order of operations and i would start there first before these more complex problems i'll drop that link down in the description and then you can try these order of operations problems if you're ready for this video let's jump into number one where we have parentheses 5 plus 7 ends parentheses times 4 minus 20. so let's go through our process or steps here and start with are there any parentheses yes so that's where we start with the 5 plus 7 in the parentheses so 5 plus 7 is 12. so i would suggest doing one step at a time and breaking these problems down until you get to that final answer so we have 12. let's bring everything else down that we did not use so the times 4 and the minus 20. so now we have multiplication and subtraction so any parentheses no any exponents no any multiplication or division yes so that's what we do next 12 times 4 is 48 bring down our subtraction sign and 20 everything we did not use and then we're left with only subtraction so that's where we end 48 minus 20 is going to give us 28 and that's our final answer so let's move on to number two where we have parentheses 9 plus 21 divided by 7 end parentheses plus 3 to the third power or 3 cubed so any parentheses yes so that's where we start now we have addition and division within those parentheses so we kind of have an order of operations problem within an order of operations problem so let's go through our steps for inside those parentheses any parentheses inside the parentheses no any exponents no any multiplication or division yes so that's where we start 21 divided by seven and that's going to give us three bring down everything we did not use and keep everything in the same exact order and we want to keep those parentheses around the nine plus three you keep the parentheses there until you solve everything within them so now let's go through our process again do we have any parentheses yes so that's what we do next nine plus three is twelve bring down everything we did not use in the same exact order and continue to go through our process so we start all over any parentheses here no any exponents yes so 3 to the power of 3 or 3 cubed that does not mean 3 times 3 it means let's move up here 3 times 3 times 3. so 3 times 3 is 9 times 3 gives us 27 so 3 cubed equals 27. bring down everything we did not use so the 12 and the addition sign and we end with 12 plus 27 which is 39. so our final answer for number two 39 on to number 3 where we have 8 parentheses 6 plus 3 ends parentheses minus 11. now i do want to mention whenever you have a number right next to a set of parentheses it's multiplication so that's 8 times 6 plus 3 in those parentheses minus 11. so let's go through our process any parentheses yes that's where we start 6 plus 3 gives us 9. bring down everything we did not use so bring down the 8 and we can put a multiplication sign in between that 8 and 9 now minus 11. make sure you use some type of symbol in between the 8 and the 9 to indicate multiplication you can't just drop the 8 down right next to the 9 because you would have 89 all right so let's go from there do we have any parentheses left no any exponents no any multiplication or division yes so that's what we do next 8 times 9 which is 72 minus 11. bring down that subtraction and the 11. so we're only left with subtraction so that's where we end so 72 minus 11 gives us 61 and we are done with number three so on to number four where we have parentheses 19 minus six plus five squared and parentheses plus parentheses 20 divided by 4 and parentheses so do we have any parentheses yes we have two sets of parentheses here so let's just work our way from left to right so we'll start with the set of parentheses on the left where we have 19 minus 6 plus 5 squared so this is one of those problems where we have order of operations within order of operations so we have subtraction addition and an exponent there so any parentheses in the parentheses no any exponents yes we have 5 squared which is not 10. it doesn't mean 5 times 2 it means 5 times 5. so let me write that out up here this means 5 times 5 that gives us 25 bring down everything we did not use keep everything in order and we'll go from there so any parentheses in those parentheses no any more exponents no any multiplication or division no any addition or subtraction yes we have both subtraction and addition now remember addition and subtraction are both level four addition is not more important or it doesn't come before subtraction they're both level four so we go left to right so we do subtraction first here 19 minus 6 which is going to give us 13. bring down everything we did not use so now we have 13 plus 25 within that set of parentheses and that would is going to give us 38 plus 20 divided by 4. so do we have any parentheses yes we have that 20 divided by 4 so that comes next 20 divided by 4 is 5. bring down everything we did not use and we end with addition 38 plus 5 which equals running out of room here 40 3. so our final answer for number 4 is 43 so there you have it there's how you solve order of operations problems i hope that helped thanks so much for watching until next time peace